A Blessing of Dimensionality: Measure Concentration and Probabilistic Inference

Pinar Muyan, Nando de Freitas
Proceedings of the Ninth International Workshop on Artificial Intelligence and Statistics, PMLR R4:217-224, 2003.

Abstract

This paper proposes an efficient sampling method for inference in probabilistic graphical models. The method exploits a blessing of dimensionality known as the concentration of measure phenomenon in order to derive analytic expressions for proposal distributions. The method can also be interpreted in a variational setting, were one minimises an upperbound on the estimator variance. The results on simple settings are very promising. We believe this method has great potential in graphical models used for diagnosis.

Cite this Paper

BibTeX
@InProceedings{pmlr-vR4-muyan03a, title = {A Blessing of Dimensionality: Measure Concentration and Probabilistic Inference}, author = {Muyan, Pinar and de Freitas, Nando}, booktitle = {Proceedings of the Ninth International Workshop on Artificial Intelligence and Statistics}, pages = {217--224}, year = {2003}, editor = {Bishop, Christopher M. and Frey, Brendan J.}, volume = {R4}, series = {Proceedings of Machine Learning Research}, month = {03--06 Jan}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/r4/muyan03a/muyan03a.pdf}, url = {https://proceedings.mlr.press/r4/muyan03a.html}, abstract = {This paper proposes an efficient sampling method for inference in probabilistic graphical models. The method exploits a blessing of dimensionality known as the concentration of measure phenomenon in order to derive analytic expressions for proposal distributions. The method can also be interpreted in a variational setting, were one minimises an upperbound on the estimator variance. The results on simple settings are very promising. We believe this method has great potential in graphical models used for diagnosis.}, note = {Reissued by PMLR on 01 April 2021.} }
Endnote
%0 Conference Paper %T A Blessing of Dimensionality: Measure Concentration and Probabilistic Inference %A Pinar Muyan %A Nando de Freitas %B Proceedings of the Ninth International Workshop on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2003 %E Christopher M. Bishop %E Brendan J. Frey %F pmlr-vR4-muyan03a %I PMLR %P 217--224 %U https://proceedings.mlr.press/r4/muyan03a.html %V R4 %X This paper proposes an efficient sampling method for inference in probabilistic graphical models. The method exploits a blessing of dimensionality known as the concentration of measure phenomenon in order to derive analytic expressions for proposal distributions. The method can also be interpreted in a variational setting, were one minimises an upperbound on the estimator variance. The results on simple settings are very promising. We believe this method has great potential in graphical models used for diagnosis. %Z Reissued by PMLR on 01 April 2021.
APA
Muyan, P. & de Freitas, N.. (2003). A Blessing of Dimensionality: Measure Concentration and Probabilistic Inference. Proceedings of the Ninth International Workshop on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research R4:217-224 Available from https://proceedings.mlr.press/r4/muyan03a.html. Reissued by PMLR on 01 April 2021.

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